In 1D cellular automata, totalistic half-distance rules can be displayed with a simple square, but much of their symmetry is lost. Some of the methods for showing their full symmetry are the shifted squares, hexagons, and disks methods. These display methods place an underlying cell between the two cells above, which is exactly what is needed when the radius is 1/2. For radii 3/2 and 5/2, the underlying cell is placed between the corresponding 4 or 6 cells.
You can control the initial condition to search for changes in shading, with extra zeros added to fill out the desired width.